teaching, math, teaching math

Disrupt Math

Look beyond the numbers. Look around and through them. Answer questions we don’t even know how to ask. The math that doesn’t exist.

-Hidden Figures

I’m fascinated by the English teacher community around #DisruptTexts. The community hosts Twitter chats during the school year as well as an ongoing conversation around disrupting the white male literary canon. One goal is to replace texts, making space for new works that help more students see themselves in the literature they read and reflect perspectives that have been excluded from the canon. A second goal is to apply a critical lens to texts that remain, looking at literary classics from new perspectives and challenging narratives by questioning the ways that groups are centered or marginalized. See this great post by Tricia Ebarvia for a deeper dive into what disrupting texts looks like.

The #DisruptTexts community came up during the Twitter Math Camp morning session “Taking a Knee in the Mathematics Classroom: Moving From Analysis to Action” led by Marian Dingle and Wendy Menard. Each of my last three years at Twitter Math Camp, there has been a lot of interest in conversations about equity. And each of those years, despite initial interest, those conversations have seemed to fizzle. I’m curious what a rich, sustained community around equity would look like in the online math education world. One thing I’ve noticed in past conversations around equity is a focus on sharing resources. Many teachers want to create or draw from a bank of social justice lessons, or share ways to help students see themselves as potential mathematicians, even if they don’t fit our culture’s stereotypes of what a mathematician looks like. And these are awesome conversations! I’ve really enjoyed them. But what I’m looking for, and what I conjecture the community as a whole would benefit from, is a space that centers learning. That’s something I love about #DisruptTexts. While it’s a space to share concrete ideas around disrupting the literary canon, it’s also a space for continuing conversations around why, exactly, it’s important to disrupt the canon, what a more inclusive English curriculum might look like, how to start tough conversations in schools, and broadly just asking questions and learning from others.

One group doing this work has been the #MTBoS book club that Annie Perkins has organized. I’ve enjoyed following along with those conversations, and I think they’ve done a lot of this work. But I’m skeptical that a book club is the best way to draw new people in — there’s a significant barrier to entry, and it by necessity moves slowly.

I’ve heard from lots of folks in the math education world that they care about equity, and they want to increase their capacity in doing equity work, but they’re not sure how, and they’re hesitant to engage because of a fear of saying the wrong thing. What would it look like to create a space that draws people in to conversations about equity and focuses on learning, while also supporting concrete change in classrooms? There are lots of great folks already doing this work. What’s missing is the core message and connecting thread to tie it all together. I’m not sure what that looks like. There are lots of pieces of math education we can critically examine. Here are a few I’d love to have conversations and learn more about.

Who practices mathematics? Sunil Singh recently wrote a great piece advocating for math history to be taught in schools to help students understand those who have contributed to mathematical knowledge but are not highlighted as mathematicians in classrooms. I just got my tote bag, thanks to Chris Nho! And Annie Perkins has done awesome work collecting information on mathematicians who aren’t just white dudes to help students see themselves as potential mathematicians.

How is mathematical knowledge created? I love Ben Blum-Smith’s piece on the history of calculus. It’s very funny, and it also gets at the uncertainty in what calculus even was, uncertainty that lasted for centuries. The math we teach in schools didn’t pop fully formed out of brilliant and reclusive mathematicians. It was constructed over long periods of time, through debate and disagreement, and many ideas that are staples of our curriculum weren’t well understood until recently. (See also, the concept of a function.)

What does it mean to practice mathematics? Is mathematics only a study of abstraction? Can it also be used for social good? Can it be used to understand inequality? Can it be used to make better informed political decisions? Is mathematics only about fast and accurate computation, or can it also be about intuition, about negotiating ambiguity, and about joy? How can we better value the ideas and perspectives that our students bring to our classrooms and build from what students already know?

I have two convictions about this work. First, there are a ton of brilliant people already sharing important ideas, but there is potential to share them more widely and create a more vibrant and ongoing conversation that centers equity in math classrooms. Second, I know I have a ton to learn, as does the larger math community, and a space that draws more people in to conversations to reconceptualize how we think of mathematics and mathematics education could have enormous value for our students.

I don’t know what it might look like. I know thoughtful people have worked on this, and I don’t mean to diminish the work of others who have tried to build an equity-oriented math community. But I want to continue conversations to question how we can do a little better, learn a little more, and reach a little farther.

Along these lines, I sometimes wonder if highlighting individual “geniuses” from other cultures is sort of reaffirming the dominant culture, even as it aims to be equity oriented.

I think an equity message might have a stronger foundation if it affirmed something like Bill Thurston’s view of math: “In short, mathematics only exists in a living community of mathematicians that spreads understanding and breaths life into ideas both old and new. The real satisfaction from mathematics is in learning from others and sharing with others.”

So I’d be interested in rejecting the idea that mathematical innovators as “best mathematicians,” and also problematizing the idea that individual mathematicians are as responsible for innovation as we think they are.

So if we’re searching for inspiration for students, I wonder if we could change the message. I’m thinking out loud here, but here is some thinking about messages I’d prefer over “great mathematical innovators aren’t just white men”:

(1) Every Culture has Mathematics [highlight e.g. Greek Proof with Mesopotamian Surveying Puzzles with Egyptian with Indian with Chinese, with an emphasis that every culture is unique and that culture influences how math is defined]

(2) Math is about spreading understanding [highlight e.g. Islamic culture passing on Greek knowledge, former slaves and children of former slaves seeking mathematical knowledge]

But more broadly, this is a way that we can narrate choices about how math class is structured — valuing collaboration and student voice — reflecting how mathematics has been constructed. Seems like a potentially powerful message.

I should really just ask Ben this, but I don’t entirely know what to make of his piece. Should it inspire us to see a deeply inequitable assumption — talent is innate, math is driven by individual geniuses — and see it applied to oppressed groups? Ben’s post raises a question that I would love to see a longer discussion of.

I’m not a purist, and I think the libel against the black mind is an urgent-enough wickedness that let’s fire on all cylinders against it. Here’s how I see it:

We all already live in a country/world where, outside of a small community of mostly math educators straining against it, the particular deeply inequitable assumption you mentioned, Michael (talent is innate, math is driven by individual genuises — actually, I’m sort of surprised to hear you call it that!) is taken as common sense. That’s a fact of life for now. One thing to do is to build and spread a new, more equitable and more truthful kind of common sense, but that’s a long-term project. Defeating the mind libel is too urgent a matter to be asked to wait for that other victory before we can even begin. More generally, I don’t want to be one to put ideological purity in front of progress in all its forms. Certainly not these days.

In that context, yay Hidden Figures! They don’t come grumpier about the lie of mathematical talent than I am. But it’s not the time to mute one’s exaltation over seeing a little black girl finally, at long last be given the Good Will Hunting treatment. People already believe that sh*t about how math works. What they don’t believe, and urgently need to, is that black people can and do do stunning things with their minds. So Hidden Figures is an easy, unambiguous net win. ALL WHITE PARENTS, PLEASE SHOW YOUR KID THIS FILM.

🙂

Does that resolve anything?

First postscript. As films about math accomplishment go, I actually found Hidden Figures comparatively low-key with the genius-fetishizing. Katherine Johnson’s super-magical-power-brain was really not the point of the film. To my surprise, I felt the same way about The Man Who Knew Infinity. It’s almost like the new ones with the historical brown mathematicians have a richer (based on a true!) story to tell and they don’t need to ride those tropes so hard.

Second postscript, somewhat more directly addressing your earlier comment about “I sometimes wonder if highlighting individual ‘geniuses’ from other cultures is sort of reaffirming the dominant culture, even as it aims to be equity oriented.” I mean, look, I personally am not going to talk about anybody’s mathematical accomplishment as “genius,” I’m 100% of the time going to make every effort to talk about it in other ways I view as more truthful, more empowering, and less mystificatory. And I’m going to encourage others to do the same. (And, imo, there is plenty of latitude inside this to highlight the important and awe-inspiring contributions of particular individuals from marginalized groups. Benjamin Banneker was such an effing bad*ss!) But meanwhile, if somebody else makes a book about black math geniuses or etc., that’s not the book I’m going to go after. In other words, I intend to be careful that where I choose to take my stand on genius-fetishizing isn’t in the way of anybody else’s equity project.

Third postscript. As I wrote the second postscript, it dawned on me that I think we’re having slightly parallel conversations. Everything I’ve said here is about public discourse. I have in mind “how are our conversations intervening into the culture at large.” Note that my most pointed plea to see HF is directed at white parents. Meanwhile, rereading your original comment above, it sort of crystallized for me that this conversation is happening in the context of you teaching at BEAMcurrently. So you’re working daily with math-engaged brown children, and you’re probably sorting through this in the context of “what messages do I want to use to empower the kids I’m seeing tomorrow.” This does recalibrate the conversation for me a bit. Would love to chat about it in person.

That’s all really helpful and I think your’e right, Ben, that I almost never think of myself as a public-facing representative of math. You’re also right that I’m thinking a lot of this right now in the context of teaching at BEAM…more on that some other time!

I used Danny Bernard Martin’s “Taking a Knee in Mathematics Education” video from the 2018 NCTM Annual to start Day 1 of the Social Justice Working Group. And I love this idea of a sustainable community about disrupting mathematics. Who’s voices are amplified? How can we amplify the missing voices? What stories are missing? Why? Where can we look to find the missing stories?

Yea! I’m thinking about that in the context of my blogging. I read a recent challenge to consider the authors that we read. Do they represent a range of perspectives? But I can ask the same questions in terms of which voices I amplify in this space — which groups are included, and which are not?